Continuous functions f, g are known to have the properties z 4 1 f(x) dx = 19, z 4 1 g(x) dx = 12 respectively. use these to find the value of the integral i = z 4 1 (8f(x) − g(x) + 7) dx. 1. i = 157 2. i = 161 3. i = 159 4. i = 163 5. i = 155

Which sum or difference identity would you use to verify that cos (180° - q) = -cos q? a.) sin (a -b) = sin a cos b – cos a sin b b.) cos (a -b) = cos a cos b – sin a sin b c.) cos (a -b) = cos a cosb + sin a sin b d.) sin (a + b) = sin a cos b + cos a sin b

Suppose you are choosing a 6-digit personal access code. this code is made up of 4 digits chosen from 1 to 9, followed by 2 letters chosen from a to z. any of these digits or letters can be repeated. find the total number of personal access codes that can be formed. 492,804 341,172 39,917,124 4,435,236

What is the domain of the of the exponential function shown below?